Wood putty can be used to fill in the hole with a putty knife. After it hardens, sand the putty flush with the surrounding surface. With a coat of paint or stain applied, the repair should be almost invisible. If the hole is large, you might want to carve a tight fitting wooden plug to take up most of the space, then use putty to fill in the gaps and cracks and hold the plug in place. Remember to give the putty proper time to dry before sanding.
Filling a mis-drilled hole in metal is similar to wood to a certain extent, except you're going to need a welding machine and some skill using it. The basic technique is to fill the hole with a plug of the same type of metal. Use the welding rod to heat the metal plug enough to shape it to the dimensions of the plug. If the hole is small enough, you might not even need a plug but could simply melt the edges of the hole enough to fill in the gap. If any of the repair protrudes above the surface, a quick hit with an angle grinder should take it down to level. Small holes in metal can also be filled with two-part epoxies, such as Bondo or JB Weld.
Welding with plastic takes more skill and practice than metal, though the method of filling a hole drilled in the wrong place is about the same. Hot-air or injection welders are the most common types of plastic welders. You need to find some filler of the same material, melt it, shape it, let it dry, and sand it. Pay more attention to the type of welding rod you're using when it comes to plastic welding. The rod must be the same type of material as the plastic you want to repair, or no bonding will occur.
The thing to keep in mind is that a mistakenly drilled hole doesn't mean you need to throw out the project and start over. Most incidents like this can be repaired. If you don't have experience with this sort of work, practice on a scrap of wood or metal with another hole before trying it on the project piece. Don't get frustrated. Don't get in a hurry.